Question: Solve for $x$ and $y$ using elimination. ${2x+2y = 32}$ ${-6x-3y = -75}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $3$ ${6x+6y = 96}$ $-6x-3y = -75$ Add the top and bottom equations together. $3y = 21$ $\dfrac{3y}{{3}} = \dfrac{21}{{3}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {2x+2y = 32}\thinspace$ to find $x$ ${2x + 2}{(7)}{= 32}$ $2x+14 = 32$ $2x+14{-14} = 32{-14}$ $2x = 18$ $\dfrac{2x}{{2}} = \dfrac{18}{{2}}$ ${x = 9}$ You can also plug ${y = 7}$ into $\thinspace {-6x-3y = -75}\thinspace$ and get the same answer for $x$ : ${-6x - 3}{(7)}{= -75}$ ${x = 9}$